Related papers: Universal conductance distribution in three dimens…
We report a careful finite size scaling study of the metal insulator transition in Anderson's model of localisation. We focus on the estimation of the critical exponent $\nu$ that describes the divergence of the localisation length. We…
The single parameter scaling hypothesis is the foundation of our understanding of the Anderson transition. However, the conductance of a disordered system is a fluctuating quantity which does not obey a one parameter scaling law. It is…
We report a numerical analysis of the Anderson transition in a quantum-chaotic system, the quasiperiodic kicked rotor with three incommensurate frequencies. It is shown that this dynamical system exhibits the same critical phenomena as the…
The two-terminal conductance of a random flux model defined on a square lattice is investigated numerically at the band center using a transfer matrix method. Due to the chiral symmetry, there exists a critical point where the ensemble…
The influence of fractal clusters of a normal phase on the dynamics of a magnetic flux trapped in a percolative superconductor is considered. The critical current distribution and the current-voltage characteristics of fractal…
We numerically study the distribution function of the conductance (transmission) in the one-dimensional tight-binding Anderson and periodic-on-average superlattice models in the region of fluctuation states where single parameter scaling is…
The zero temperature transport properties of two-dimensional lattice systems with static random magnetic flux per plaquette and zero mean are investigated numerically. We study the two-terminal conductance and its dependence on energy,…
We study analytically the metal-insulator transition in a disordered conductor by combining the self-consistent theory of localization with the one parameter scaling theory. We provide explicit expressions of the critical exponents and the…
The level statistics in the two dimensional disordered electron systems in magnetic fields (unitary ensemble) or in the presence of strong spin-orbit scattering (symplectic ensemble) are investigated at the Anderson transition points. The…
Anderson transition of the phonon modes is studied numerically. The critical exponent for the divergence of the localization length is estimated using the transfer matrix method, and the statistics of the modes is analyzed. The latter is…
Critical fluctuations of wave functions and energy levels at the Anderson transition are studied for the family of the critical power-law random banded matrix ensembles. It is shown that the distribution functions of the inverse…
Symmetry breaking surface fields give rise to nontrivial and long-ranged order parameter profiles for critical systems such as fluids, alloys or magnets confined to wedges. We discuss the properties of the corresponding universal scaling…
We consider the breakdown of conformal and scale invariance in random systems with strongly random critical points. Extending previous results on one-dimensional systems, we provide an example of a three-dimensional system which has a…
A review of recent progress in numerical studies of the Anderson transition in three dimensional systems is presented. From high precision calculations the critical exponent $\nu$ for the divergence of the localization length is estimated…
Continuous phase transitions are studied in a two dimensional nonequilibrium model with an infinite number of absorbing configurations. Spreading from a localized source is characterized by nonuniversal critical exponents, which vary…
We consider wires near a zero temperature transition between superconducting and metallic states. The critical theory obeys hyperscaling, which leads to a universal frequency, temperature, and length dependence of the conductance; quantum…
The critical behaviour of 3-dimensional disordered systems in a strong magnetic field is investigated by analysing the spectral fluctuations of the energy spectrum. The level spacing distribution $P(s)$ as well the Dyson-Mehta statistics…
We investigated numerically the distribution of participation numbers in the 3d Anderson tight-binding model at the localization-delocalization threshold. These numbers in {\em one} disordered system experience strong level-to-level…
We investigate the finite-size scaling of the boundary quantum geometric tensor (QGT) numerically close to the Anderson localization transition in the presence of small external magnetic fields. The QGT exhibits universal scaling and…
The critical exponents for the Anderson transition in three and four effective dimensions are discussed on the basis of previous data obtained for the frequency modulated kicked rotator. Without appeal to a scaling function they are shown…